Related papers: Predictive density estimators with integrated $L_1…
We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K $\ge$ 2 independent copies of X. We provide a constructive estimator based on a suitable definition of…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and type-II losses, we prove the logarithmic asymptotic $$ L_n^* =…
Weakly chaotic maps with unstable fixed points are investigated in the regime where the invariant density is non-normalizable. We propose that the infinite invariant density of these maps can be estimated using as the long time limit of…
We revisit the numerical calculation of generalized Lyapunov exponents, $L$($q$), in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then $L$($q$)…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
Consider a density $f$ on $[0,1]$ that must be estimated from an i.i.d. sample $X_1,...,X_n$ drawn from $f$. In this note, we study binary-tree-based histogram estimates that use recursive splitting of intervals. If the decision to split an…
The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly…
Consider the problem of estimating a random variable $X$ from noisy observations $Y = X+ Z$, where $Z$ is standard normal, under the $L^1$ fidelity criterion. It is well known that the optimal Bayesian estimator in this setting is the…
Leave-one-out (LOO) prediction provides a principled, data-dependent measure of generalization, yet guarantees in fully transductive settings remain poorly understood beyond specialized models. We introduce Median of Level-Set Aggregation…
This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…
Bandwidth selection is crucial in the kernel estimation of density level sets. A risk based on the symmetric difference between the estimated and true level sets is usually used to measure their proximity. In this paper we provide an…